arXiv subjects

Tolga Özaslan

Publications and source records attributed to Tolga Özaslan.

2 recordsLinked to original sources

arXiv2026

H-BRICK: Hierarchical Boundary Reachability Index with Compressed Kleene Closure for Directed Grid Graphs

Repeated directed reachability queries arise in online path planning, task-agent allocation, and swarm control on static grid maps, where reachability is asymmetric and full transitive closure is storage-prohibitive. We introduce H-BRICK, a Hierarchical Boundary Reachability Index with Compressed Kleene closure for exact cell-to-cell queries on directed grid graphs. H-BRICK partitions the graph into tiles, computes a local Boolean Kleene closure within each tile, and projects it onto the tile's boundary ports. The resulting directed port-to-port summaries are then composed recursively across shared interfaces up to a single root covering the graph. We prove algebraically that the construction is exact: in the Boolean Kleene algebra of binary relations, every composed summary equals the boundary projection of the regional reflexive transitive closure, and every cell-to-cell query agrees with reachability in the original graph. Experiments on directed grid graphs across diverse map topologies compare H-BRICK against directed search and component-based baselines, and compare its storage requirements against full transitive closure. A batched reachability evaluation further demonstrates that sharing endpoint lifts across many-source/many-target queries amortizes hierarchical traversal and, at k=64, yields a 5.0x-22.9x throughput improvement over the scalar query loop. The results show that hierarchical boundary compression is most advantageous in query-intensive spatial graphs where online search traverses large reachable regions and the hierarchy maintains compact boundary interfaces.

cs.RO↗

arXiv2026

H-TRIP: Exact Many-to-Many Distance Index for Multi-Robot Exploration

Frontier-based exploration systems repeatedly evaluate geodesic travel costs between robot poses and candidate viewpoints, and tour-based planners consume the full pairwise distance matrix built from them. Recomputing these matrices with one graph search per source scales with the explored map size, whereas distance caches that refresh only locally affected or newly created frontiers can retain stale costs between surviving pairs when newly discovered free space creates a global shortcut. We present H-TRIP (Hierarchical Tropical Rank-one Incremental Propagation), an exact distance index grounded in Kleene algebra over the min-plus semiring for monotonically growing occupancy grids. H-TRIP partitions the known map into a spatial hierarchy with fixed boundary ports. Each unknown-to-free revelation is decomposed into efficient rank-one min-plus edge insertions at the affected leaf, and only decreased port-to-port summaries are propagated along its ancestor chain. A shared hierarchical lift evaluates the dense many-to-many matrix of shortest distances for all active query points on the occupancy map. We prove that sequential insertions preserve exact shortest-path distances on the grid. Benchmark experiments confirm exact agreement with reference searches on fully built maps and show that dense many-to-many queries at a few dozen viewpoints are up to two orders of magnitude faster than sequential k x BFS. On exploration runs with sixteen robots, in-loop queries on the growing occupancy graph are 2.21x-8.59x faster than co-scheduled k x BFS on maps with side 256, 512, and 1024 cells.

cs.RO↗